The government has given the UK newspaper industry three days to get behind its plans for press regulation in a high-risk strategy that could see some of the country's biggest publishers go it alone with their own watchdog.

Culture secretary Maria Miller confirmed in an official statement to MPs in the Commons on Tuesday afternoon that the government was rejecting the newspaper publishers' plans for a regulator because they lacked sufficient independence.

Miller said that the industry's plans did not comply with some of the "fundamental principles" of the Leveson report, including those on independence and access to arbitration.

The cross-party proposals for a new press regulator underpinned by royal charter agreed by the Conservatives, Liberal Democrats, Labour and Hacked Off – the group that campaigns for tighter regulation – will now be put forward for approval at a specially convened meeting of the privy council on 30 October.

The final draft text will be published in Friday.

"The proposals we are discussing are all about redress for the public but it's also about retaining freedom of the press which wll all value so highly," said Miller.

Les Hinton, the former chief executive of News International, owner of the Times and the Sun, and friend of Rupert Murdoch, said the solution made his heart sink.

"Sitting in the land of the First Amendment watching the House of Commons discuss press 'self' regulation. My heart sinks. Shameful," New York-based Hinton said on Twitter.

Miller said that all three parties will work together in the next few days to agree a number of changes to the text agreed in March and produce a final draft of the cross-party charter.

However, in an answer to Labour deputy leader Harriet Harman, she made clear that this were more likely to revolve around issues such as the addition of a clause that would implement the cross-party charter in Scotland.

Miller indicated there are also likely to be some concessions on a new arbitration unit, which local newspapers have said could trigger a new industry of "ambulance-chasing" lawyers looking for cash compensation from titles already struggling for survival.

In a three-page letter also published on Tuesday afternoon, Miller's Department for Culture Media and Sport said there were "areas it finds acceptable" in the industry plan but it "falls short of government policy on the self-regulation of the press" because it was too inextricably linked with the newspaper publishers that would fund the body.

One newspaper executive said the backers of the industry regulator did not believe the rejection was "crushing" and it "left the door open for more talks".

However, this was before Miller announced that the final cross-party charter would be published on Friday and if there was not agreement across the political spectrum the government would return to the original plan signed on 18 March, which most of the press industry vehemently opposed.

Speaking before Miller's Commons statement, Sun columnist Trevor Kavanagh said he believed the big newspaper groups would press ahead with their plans for the Independent Press Standards Organisation, the proposed replacement for the Press Complaints Commission. "We are not prepared to sign up to a charter in which politicans get their sticky fingers into regulation. Until the waters become clear we will proceed with IPSO," Kavanagh told the Guardian.

He said the royal charter devised by the government would sweep aside 300 years of press freedom because it would give politicians a mechanism to interfere.

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